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<h1><img src="../../../../boost.png" align="middle" />Sparse Matricies</h1>
<div class="toc" id="toc"></div>
<h2><a name="mapped_matrix"></a>Mapped Matrix</h2>
<h4>Description</h4>
<p>The templated class <code>mapped_matrix&lt;T, F, A&gt;</code> is
the base container adaptor for sparse matricies using element maps.
For a <em>(m xn</em>)-dimensional sparse matrix and <em>0 &lt;= i &lt; m</em>,
<em>0 &lt;= j &lt; n</em> the non-zero elements
<em>m</em><sub><em>i, j</em></sub> are mapped via <em>(i x n +
j)</em> for row major orientation or via <em>(i + j x m)</em> for
column major orientation to consecutive elements of the associative
container, i.e. for elements <em>k</em> =
<em>m</em><sub><em>i</em></sub><sub><sub><em>1</em></sub></sub><sub>
<em>,j</em></sub><sub><sub><em>1</em></sub></sub>and <em>k + 1 =
m</em><sub><em>i</em></sub><sub><sub><em>2</em></sub></sub><sub><em>
,j</em></sub><sub><sub><em>2</em></sub></sub>of the container holds
<em>i</em><sub><em>1</em></sub> <em>&lt;
i</em><sub><em>2</em></sub> or <em>(i</em><sub><em>1</em></sub>
<em>= i</em><sub><em>2</em></sub> and
<em>j</em><sub><em>1</em></sub> <em>&lt;
j</em><sub><em>2</em></sub><em>)</em> with row major orientation or
<em>j</em><sub><em>1</em></sub> <em>&lt;
j</em><sub><em>2</em></sub> or <em>(j</em><sub><em>1</em></sub>
<em>= j</em><sub><em>2</em></sub> and
<em>i</em><sub><em>1</em></sub> <em>&lt;
i</em><sub><em>2</em></sub><em>)</em> with column major
orientation.</p>
<h4>Example</h4>
<pre>
#include &lt;boost/numeric/ublas/matrix_sparse.hpp&gt;
#include &lt;boost/numeric/ublas/io.hpp&gt;

int main () {
    using namespace boost::numeric::ublas;
    mapped_matrix&lt;double&gt; m (3, 3, 3 * 3);
    for (unsigned i = 0; i &lt; m.size1 (); ++ i)
        for (unsigned j = 0; j &lt; m.size2 (); ++ j)
            m (i, j) = 3 * i + j;
    std::cout &lt;&lt; m &lt;&lt; std::endl;
}
</pre>
<h4>Definition</h4>
<p>Defined in the header matrix_sparse.hpp.</p>
<h4>Template parameters</h4>
<table border="1" summary="parameters">
<tbody>
<tr>
<th>Parameter</th>
<th>Description</th>
<th>Default</th>
</tr>
<tr>
<td><code>T</code></td>
<td>The type of object stored in the mapped matrix.</td>
<td></td>
</tr>
<tr>
<td><code>F</code></td>
<td>Functor describing the storage organization. <a href=
"#mapped_matrix_1">[1]</a></td>
<td><code>row_major</code></td>
</tr>
<tr>
<td><code>A</code></td>
<td>The type of the adapted array. <a href=
"#mapped_matrix_2">[2]</a></td>
<td><code>map_std&lt;std::size_t, T&gt;</code></td>
</tr>
</tbody>
</table>
<h4>Model of</h4>
<p><a href="container_concept.html#matrix">Matrix</a> .</p>
<h4>Type requirements</h4>
<p>None, except for those imposed by the requirements of <a href=
"container_concept.html#matrix">Matrix</a> .</p>
<h4>Public base classes</h4>
<p><code>matrix_container&lt;mapped_matrix&lt;T, F, A&gt;
&gt;</code></p>
<h4>Members</h4>
<table border="1" summary="members">
<tbody>
<tr>
<th>Member</th>
<th>Description</th>
</tr>
<tr>
<td><code>mapped_matrix ()</code></td>
<td>Allocates a <code>mapped_matrix</code> that holds at most zero
rows of zero elements.</td>
</tr>
<tr>
<td><code>mapped_matrix (size_type size1, size_type2, size_type non_zeros = 0)</code></td>
<td>Allocates a <code>mapped_matrix</code> that holds at most
<code>size1</code> rows of <code>size2</code> elements.</td>
</tr>
<tr>
<td><code>mapped_matrix (const mapped_matrix &amp;m)</code></td>
<td>The copy constructor.</td>
</tr>
<tr>
<td><code>template&lt;class AE&gt;<br />
mapped_matrix (size_type non_zeros, const
matrix_expression&lt;AE&gt; &amp;ae)</code></td>
<td>The extended copy constructor.</td>
</tr>
<tr>
<td><code>void resize (size_type size1, size_type size2, bool preserve = true)</code></td>
<td>Reallocates a <code>mapped_matrix</code> to hold at most
<code>size1</code> rows of <code>size2</code> elements. The
existing elements of the <code>mapped_matrix</code> are preseved
when specified.</td>
</tr>
<tr>
<td><code>size_type size1 () const</code></td>
<td>Returns the number of rows.</td>
</tr>
<tr>
<td><code>size_type size2 () const</code></td>
<td>Returns the number of columns.</td>
</tr>
<tr>
<td><code>const_reference operator () (size_type i, size_type j)
const</code></td>
<td>Returns the value of the <code>j</code>-th element in the
<code>i</code>-th row.</td>
</tr>
<tr>
<td><code>reference operator () (size_type i, size_type
j)</code></td>
<td>Returns a reference of the <code>j</code>-th element in the
<code>i</code>-th row.</td>
</tr>
<tr>
<td><code>mapped_matrix &amp;operator = (const mapped_matrix
&amp;m)</code></td>
<td>The assignment operator.</td>
</tr>
<tr>
<td><code>mapped_matrix &amp;assign_temporary (mapped_matrix
&amp;m)</code></td>
<td>Assigns a temporary. May change the mapped matrix
<code>m</code> .</td>
</tr>
<tr>
<td><code>template&lt;class AE&gt;<br />
mapped_matrix &amp;operator = (const matrix_expression&lt;AE&gt;
&amp;ae)</code></td>
<td>The extended assignment operator.</td>
</tr>
<tr>
<td><code>template&lt;class AE&gt;<br />
mapped_matrix &amp;assign (const matrix_expression&lt;AE&gt;
&amp;ae)</code></td>
<td>Assigns a matrix expression to the mapped matrix. Left and
right hand side of the assignment should be independent.</td>
</tr>
<tr>
<td><code>template&lt;class AE&gt;<br />
mapped_matrix &amp;operator += (const matrix_expression&lt;AE&gt;
&amp;ae)</code></td>
<td>A computed assignment operator. Adds the matrix expression to
the mapped matrix.</td>
</tr>
<tr>
<td><code>template&lt;class AE&gt;<br />
mapped_matrix &amp;plus_assign (const matrix_expression&lt;AE&gt;
&amp;ae)</code></td>
<td>Adds a matrix expression to the mapped matrix. Left and right
hand side of the assignment should be independent.</td>
</tr>
<tr>
<td><code>template&lt;class AE&gt;<br />
mapped_matrix &amp;operator -= (const matrix_expression&lt;AE&gt;
&amp;ae)</code></td>
<td>A computed assignment operator. Subtracts the matrix expression
from the mapped matrix.</td>
</tr>
<tr>
<td><code>template&lt;class AE&gt;<br />
mapped_matrix &amp;minus_assign (const matrix_expression&lt;AE&gt;
&amp;ae)</code></td>
<td>Subtracts a matrix expression from the mapped matrix. Left and
right hand side of the assignment should be independent.</td>
</tr>
<tr>
<td><code>template&lt;class AT&gt;<br />
mapped_matrix &amp;operator *= (const AT &amp;at)</code></td>
<td>A computed assignment operator. Multiplies the mapped matrix
with a scalar.</td>
</tr>
<tr>
<td><code>template&lt;class AT&gt;<br />
mapped_matrix &amp;operator /= (const AT &amp;at)</code></td>
<td>A computed assignment operator. Divides the mapped matrix
through a scalar.</td>
</tr>
<tr>
<td><code>void swap (mapped_matrix &amp;m)</code></td>
<td>Swaps the contents of the mapped matrices.</td>
</tr>
<tr>
<td><code>true_refrence insert_element (size_type i, size_type j, const_reference
t)</code></td>
<td>Inserts the value <code>t</code> at the <code>j</code>-th
element of the <code>i</code>-th row. Duplicates elements are not allowed.</td>
</tr>
<tr>
<td><code>void erase_element (size_type i, size_type j)</code></td>
<td>Erases the value at the <code>j</code>-th element of the
<code>i</code>-th row.</td>
</tr>
<tr>
<td><code>void clear ()</code></td>
<td>Clears the mapped matrix.</td>
</tr>
<tr>
<td><code>const_iterator1 begin1 () const</code></td>
<td>Returns a <code>const_iterator1</code> pointing to the
beginning of the <code>mapped_matrix</code>.</td>
</tr>
<tr>
<td><code>const_iterator1 end1 () const</code></td>
<td>Returns a <code>const_iterator1</code> pointing to the end of
the <code>mapped_matrix</code>.</td>
</tr>
<tr>
<td><code>iterator1 begin1 ()</code></td>
<td>Returns a <code>iterator1</code> pointing to the beginning of
the <code>mapped_matrix</code>.</td>
</tr>
<tr>
<td><code>iterator1 end1 ()</code></td>
<td>Returns a <code>iterator1</code> pointing to the end of the
<code>mapped_matrix</code>.</td>
</tr>
<tr>
<td><code>const_iterator2 begin2 () const</code></td>
<td>Returns a <code>const_iterator2</code> pointing to the
beginning of the <code>mapped_matrix</code>.</td>
</tr>
<tr>
<td><code>const_iterator2 end2 () const</code></td>
<td>Returns a <code>const_iterator2</code> pointing to the end of
the <code>mapped_matrix</code>.</td>
</tr>
<tr>
<td><code>iterator2 begin2 ()</code></td>
<td>Returns a <code>iterator2</code> pointing to the beginning of
the <code>mapped_matrix</code>.</td>
</tr>
<tr>
<td><code>iterator2 end2 ()</code></td>
<td>Returns a <code>iterator2</code> pointing to the end of the
<code>mapped_matrix</code>.</td>
</tr>
<tr>
<td><code>const_reverse_iterator1 rbegin1 () const</code></td>
<td>Returns a <code>const_reverse_iterator1</code> pointing to the
beginning of the reversed <code>mapped_matrix</code>.</td>
</tr>
<tr>
<td><code>const_reverse_iterator1 rend1 () const</code></td>
<td>Returns a <code>const_reverse_iterator1</code> pointing to the
end of the reversed <code>mapped_matrix</code>.</td>
</tr>
<tr>
<td><code>reverse_iterator1 rbegin1 ()</code></td>
<td>Returns a <code>reverse_iterator1</code> pointing to the
beginning of the reversed <code>mapped_matrix</code>.</td>
</tr>
<tr>
<td><code>reverse_iterator1 rend1 ()</code></td>
<td>Returns a <code>reverse_iterator1</code> pointing to the end of
the reversed <code>mapped_matrix</code>.</td>
</tr>
<tr>
<td><code>const_reverse_iterator2 rbegin2 () const</code></td>
<td>Returns a <code>const_reverse_iterator2</code> pointing to the
beginning of the reversed <code>mapped_matrix</code>.</td>
</tr>
<tr>
<td><code>const_reverse_iterator2 rend2 () const</code></td>
<td>Returns a <code>const_reverse_iterator2</code> pointing to the
end of the reversed <code>mapped_matrix</code>.</td>
</tr>
<tr>
<td><code>reverse_iterator2 rbegin2 ()</code></td>
<td>Returns a <code>reverse_iterator2</code> pointing to the
beginning of the reversed <code>mapped_matrix</code>.</td>
</tr>
<tr>
<td><code>reverse_iterator2 rend2 ()</code></td>
<td>Returns a <code>reverse_iterator2</code> pointing to the end of
the reversed <code>mapped_matrix</code>.</td>
</tr>
</tbody>
</table>
<h4>Notes</h4>
<p><a name="mapped_matrix_1">[1]</a> Supported
parameters for the storage organization are <code>row_major</code>
and <code>column_major</code>.</p>
<p><a name="mapped_matrix_2">[2]</a> Supported
parameters for the adapted array are
<code>map_array&lt;std::size_t, T&gt;</code> and
<code>map_std&lt;std::size_t, T&gt;</code>. The latter is
equivalent to <code>std::map&lt;std::size_t, T&gt;</code>.</p>
<h2><a name="compressed_matrix"></a>Compressed Matrix</h2>
<h4>Description</h4>
<p>The templated class <code>compressed_matrix&lt;T, F, IB, IA,
TA&gt;</code> is the base container adaptor for compressed
matrices. For a <em>(m x n</em> )-dimensional compressed matrix and
<em>0 &lt;= i &lt; m</em>, <em>0 &lt;= j &lt; n</em> the non-zero
elements <em>m</em><sub><em>i, j</em></sub> are mapped via <em>(i x
n + j)</em> for row major orientation or via <em>(i + j x m)</em>
for column major orientation to consecutive elements of the index
and value containers, i.e. for elements <em>k</em> =
<em>m</em><sub><em>i</em></sub><sub><sub><em>1</em></sub></sub><sub>
<em>,j</em></sub><sub><sub><em>1</em></sub></sub>and <em>k + 1 =
m</em><sub><em>i</em></sub><sub><sub><em>2</em></sub></sub><sub><em>
,j</em></sub><sub><sub><em>2</em></sub></sub>of the container holds
<em>i</em><sub><em>1</em></sub> <em>&lt;
i</em><sub><em>2</em></sub> or <em>(i</em><sub><em>1</em></sub>
<em>= i</em><sub><em>2</em></sub> and
<em>j</em><sub><em>1</em></sub> <em>&lt;
j</em><sub><em>2</em></sub><em>)</em> with row major orientation or
<em>j</em><sub><em>1</em></sub> <em>&lt;
j</em><sub><em>2</em></sub> or <em>(j</em><sub><em>1</em></sub>
<em>= j</em><sub><em>2</em></sub> and
<em>i</em><sub><em>1</em></sub> <em>&lt;
i</em><sub><em>2</em></sub><em>)</em> with column major
orientation.</p>
<h4>Example</h4>
<pre>
#include &lt;boost/numeric/ublas/matrix_sparse.hpp&gt;
#include &lt;boost/numeric/ublas/io.hpp&gt;

int main () {
    using namespace boost::numeric::ublas;
    compressed_matrix&lt;double&gt; m (3, 3, 3 * 3);
    for (unsigned i = 0; i &lt; m.size1 (); ++ i)
        for (unsigned j = 0; j &lt; m.size2 (); ++ j)
            m (i, j) = 3 * i + j;
    std::cout &lt;&lt; m &lt;&lt; std::endl;
}
</pre>
<h4>Definition</h4>
<p>Defined in the header matrix_sparse.hpp.</p>
<h4>Template parameters</h4>
<table border="1" summary="parameters">
<tbody>
<tr>
<th>Parameter</th>
<th>Description</th>
<th>Default</th>
</tr>
<tr>
<td><code>T</code></td>
<td>The type of object stored in the compressed matrix.</td>
<td></td>
</tr>
<tr>
<td><code>F</code></td>
<td>Functor describing the storage organization. <a href=
"#compressed_matrix_1">[1]</a></td>
<td><code>row_major</code></td>
</tr>
<tr>
<td><code>IB</code></td>
<td>The index base of the compressed vector. <a href=
"#compressed_matrix_2">[2]</a></td>
<td><code>0</code></td>
</tr>
<tr>
<td><code>IA</code></td>
<td>The type of the adapted array for indices. <a href=
"#compressed_matrix_3">[3]</a></td>
<td><code>unbounded_array&lt;std::size_t&gt;</code></td>
</tr>
<tr>
<td><code>TA</code></td>
<td>The type of the adapted array for values. <a href=
"#compressed_matrix_3">[3]</a></td>
<td><code>unbounded_array&lt;T&gt;</code></td>
</tr>
</tbody>
</table>
<h4>Model of</h4>
<p><a href="container_concept.html#matrix">Matrix</a> .</p>
<h4>Type requirements</h4>
<p>None, except for those imposed by the requirements of <a href=
"container_concept.html#matrix">Matrix</a> .</p>
<h4>Public base classes</h4>
<p><code>matrix_container&lt;compressed_matrix&lt;T, F, IB, IA,
TA&gt; &gt;</code></p>
<h4>Members</h4>
<table border="1" summary="members">
<tbody>
<tr>
<th>Member</th>
<th>Description</th>
</tr>
<tr>
<td><code>compressed_matrix ()</code></td>
<td>Allocates a <code>compressed_matrix</code> that holds at most
zero rows of zero elements.</td>
</tr>
<tr>
<td><code>compressed_matrix (size_type size1, size_type2, size_type non_zeros = 0)</code></td>
<td>Allocates a <code>compressed_matrix</code> that holds at most
<code>size1</code> rows of <code>size2</code> elements.</td>
</tr>
<tr>
<td><code>compressed_matrix (const compressed_matrix
&amp;m)</code></td>
<td>The copy constructor.</td>
</tr>
<tr>
<td><code>template&lt;class AE&gt;<br />
compressed_matrix (size_type non_zeros, const
matrix_expression&lt;AE&gt; &amp;ae)</code></td>
<td>The extended copy constructor.</td>
</tr>
<tr>
<td><code>void resize (size_type size1, size_type size2, bool preserve = true)</code></td>
<td>Reallocates a <code>compressed_matrix</code> to hold at most
<code>size1</code> rows of <code>size2</code> elements. The
existing elements of the <code>compressed_matrix</code> are
preseved when specified.</td>
</tr>
<tr>
<td><code>size_type size1 () const</code></td>
<td>Returns the number of rows.</td>
</tr>
<tr>
<td><code>size_type size2 () const</code></td>
<td>Returns the number of columns.</td>
</tr>
<tr>
<td><code>const_reference operator () (size_type i, size_type j)
const</code></td>
<td>Returns the value of the <code>j</code>-th element in the
<code>i</code>-th row.</td>
</tr>
<tr>
<td><code>reference operator () (size_type i, size_type
j)</code></td>
<td>Returns a reference of the <code>j</code>-th element in the
<code>i</code>-th row.</td>
</tr>
<tr>
<td><code>compressed_matrix &amp;operator = (const
compressed_matrix &amp;m)</code></td>
<td>The assignment operator.</td>
</tr>
<tr>
<td><code>compressed_matrix &amp;assign_temporary
(compressed_matrix &amp;m)</code></td>
<td>Assigns a temporary. May change the compressed matrix
<code>m</code>.</td>
</tr>
<tr>
<td><code>template&lt;class AE&gt;<br />
compressed_matrix &amp;operator = (const
matrix_expression&lt;AE&gt; &amp;ae)</code></td>
<td>The extended assignment operator.</td>
</tr>
<tr>
<td><code>template&lt;class AE&gt;<br />
compressed_matrix &amp;assign (const matrix_expression&lt;AE&gt;
&amp;ae)</code></td>
<td>Assigns a matrix expression to the compressed matrix. Left and
right hand side of the assignment should be independent.</td>
</tr>
<tr>
<td><code>template&lt;class AE&gt;<br />
compressed_matrix &amp;operator += (const
matrix_expression&lt;AE&gt; &amp;ae)</code></td>
<td>A computed assignment operator. Adds the matrix expression to
the compressed matrix.</td>
</tr>
<tr>
<td><code>template&lt;class AE&gt;<br />
compressed_matrix &amp;plus_assign (const
matrix_expression&lt;AE&gt; &amp;ae)</code></td>
<td>Adds a matrix expression to the compressed matrix. Left and
right hand side of the assignment should be independent.</td>
</tr>
<tr>
<td><code>template&lt;class AE&gt;<br />
compressed_matrix &amp;operator -= (const
matrix_expression&lt;AE&gt; &amp;ae)</code></td>
<td>A computed assignment operator. Subtracts the matrix expression
from the compressed matrix.</td>
</tr>
<tr>
<td><code>template&lt;class AE&gt;<br />
compressed_matrix &amp;minus_assign (const
matrix_expression&lt;AE&gt; &amp;ae)</code></td>
<td>Subtracts a matrix expression from the compressed matrix. Left
and right hand side of the assignment should be independent.</td>
</tr>
<tr>
<td><code>template&lt;class AT&gt;<br />
compressed_matrix &amp;operator *= (const AT &amp;at)</code></td>
<td>A computed assignment operator. Multiplies the compressed
matrix with a scalar.</td>
</tr>
<tr>
<td><code>template&lt;class AT&gt;<br />
compressed_matrix &amp;operator /= (const AT &amp;at)</code></td>
<td>A computed assignment operator. Divides the compressed matrix
through a scalar.</td>
</tr>
<tr>
<td><code>void swap (compressed_matrix &amp;m)</code></td>
<td>Swaps the contents of the compressed matrices.</td>
</tr>
<tr>
<td><code>true_reference insert_element (size_type i, size_type j, const_reference
t)</code></td>
<td>Inserts the value <code>t</code> at the <code>j</code>-th
element of the <code>i</code>-th row. Duplicates elements are not allowed.</td>
</tr>
<tr>
<td><code>void erase_element (size_type i, size_type j)</code></td>
<td>Erases the value at the <code>j</code>-th element of the
<code>i</code>-th row.</td>
</tr>
<tr>
<td><code>void clear ()</code></td>
<td>Clears the compressed matrix.</td>
</tr>
<tr>
<td><code>const_iterator1 begin1 () const</code></td>
<td>Returns a <code>const_iterator1</code> pointing to the
beginning of the <code>compressed_matrix</code>.</td>
</tr>
<tr>
<td><code>const_iterator1 end1 () const</code></td>
<td>Returns a <code>const_iterator1</code> pointing to the end of
the <code>compressed_matrix</code>.</td>
</tr>
<tr>
<td><code>iterator1 begin1 ()</code></td>
<td>Returns a <code>iterator1</code> pointing to the beginning of
the <code>compressed_matrix</code>.</td>
</tr>
<tr>
<td><code>iterator1 end1 ()</code></td>
<td>Returns a <code>iterator1</code> pointing to the end of the
<code>compressed_matrix</code>.</td>
</tr>
<tr>
<td><code>const_iterator2 begin2 () const</code></td>
<td>Returns a <code>const_iterator2</code> pointing to the
beginning of the <code>compressed_matrix</code>.</td>
</tr>
<tr>
<td><code>const_iterator2 end2 () const</code></td>
<td>Returns a <code>const_iterator2</code> pointing to the end of
the <code>compressed_matrix</code>.</td>
</tr>
<tr>
<td><code>iterator2 begin2 ()</code></td>
<td>Returns a <code>iterator2</code> pointing to the beginning of
the <code>compressed_matrix</code>.</td>
</tr>
<tr>
<td><code>iterator2 end2 ()</code></td>
<td>Returns a <code>iterator2</code> pointing to the end of the
<code>compressed_matrix</code>.</td>
</tr>
<tr>
<td><code>const_reverse_iterator1 rbegin1 () const</code></td>
<td>Returns a <code>const_reverse_iterator1</code> pointing to the
beginning of the reversed <code>compressed_matrix</code>.</td>
</tr>
<tr>
<td><code>const_reverse_iterator1 rend1 () const</code></td>
<td>Returns a <code>const_reverse_iterator1</code> pointing to the
end of the reversed <code>compressed_matrix</code>.</td>
</tr>
<tr>
<td><code>reverse_iterator1 rbegin1 ()</code></td>
<td>Returns a <code>reverse_iterator1</code> pointing to the
beginning of the reversed <code>compressed_matrix</code>.</td>
</tr>
<tr>
<td><code>reverse_iterator1 rend1 ()</code></td>
<td>Returns a <code>reverse_iterator1</code> pointing to the end of
the reversed <code>compressed_matrix</code>.</td>
</tr>
<tr>
<td><code>const_reverse_iterator2 rbegin2 () const</code></td>
<td>Returns a <code>const_reverse_iterator2</code> pointing to the
beginning of the reversed <code>compressed_matrix</code>.</td>
</tr>
<tr>
<td><code>const_reverse_iterator2 rend2 () const</code></td>
<td>Returns a <code>const_reverse_iterator2</code> pointing to the
end of the reversed <code>compressed_matrix</code>.</td>
</tr>
<tr>
<td><code>reverse_iterator2 rbegin2 ()</code></td>
<td>Returns a <code>reverse_iterator2</code> pointing to the
beginning of the reversed <code>compressed_matrix</code>.</td>
</tr>
<tr>
<td><code>reverse_iterator2 rend2 ()</code></td>
<td>Returns a <code>reverse_iterator2</code> pointing to the end of
the reversed <code>compressed_matrix</code>.</td>
</tr>
</tbody>
</table>
<h4>Notes</h4>
<p><a name="compressed_matrix_1">[1]</a>
Supported parameters for the storage organization are
<code>row_major</code> and <code>column_major</code>.</p>
<p><a name="compressed_matrix_2">[2]</a>
Supported parameters for the index base are <code>0</code> and
<code>1</code> at least.</p>
<p><a name="compressed_matrix_3">[3]</a>
Supported parameters for the adapted array are
<code>unbounded_array&lt;&gt;</code> ,
<code>bounded_array&lt;&gt;</code> and
<code>std::vector&lt;&gt;</code> .</p>
<h2><a name="coordinate_matrix"></a>Coordinate Matrix</h2>
<h4>Description</h4>
<p>The templated class <code>coordinate_matrix&lt;T, F, IB, IA,
TA&gt;</code> is the base container adaptor for compressed
matrices. For a <em>(m x n</em> )-dimensional sorted coordinate
matrix and <em>0 &lt;= i &lt; m</em>, <em>0 &lt;= j &lt; n</em> the
non-zero elements <em>m</em><sub><em>i, j</em></sub> are mapped via
<em>(i x n + j)</em> for row major orientation or via <em>(i + j x
m)</em> for column major orientation to consecutive elements of the
index and value containers, i.e. for elements <em>k</em> =
<em>m</em><sub><em>i</em></sub><sub><sub><em>1</em></sub></sub><sub>
<em>,j</em></sub><sub><sub><em>1</em></sub></sub>and <em>k + 1 =
m</em><sub><em>i</em></sub><sub><sub><em>2</em></sub></sub><sub><em>
,j</em></sub><sub><sub><em>2</em></sub></sub>of the container holds
<em>i</em><sub><em>1</em></sub> <em>&lt;
i</em><sub><em>2</em></sub> or <em>(i</em><sub><em>1</em></sub>
<em>= i</em><sub><em>2</em></sub> and
<em>j</em><sub><em>1</em></sub> <em>&lt;
j</em><sub><em>2</em></sub><em>)</em> with row major orientation or
<em>j</em><sub><em>1</em></sub> <em>&lt;
j</em><sub><em>2</em></sub> or <em>(j</em><sub><em>1</em></sub>
<em>= j</em><sub><em>2</em></sub> and
<em>i</em><sub><em>1</em></sub> <em>&lt;
i</em><sub><em>2</em></sub><em>)</em> with column major
orientation.</p>
<h4>Example</h4>
<pre>
#include &lt;boost/numeric/ublas/matrix_sparse.hpp&gt;
#include &lt;boost/numeric/ublas/io.hpp&gt;

int main () {
    using namespace boost::numeric::ublas;
    coordinate_matrix&lt;double&gt; m (3, 3, 3 * 3);
    for (unsigned i = 0; i &lt; m.size1 (); ++ i)
        for (unsigned j = 0; j &lt; m.size2 (); ++ j)
            m (i, j) = 3 * i + j;
    std::cout &lt;&lt; m &lt;&lt; std::endl;
}
</pre>
<h4>Definition</h4>
<p>Defined in the header matrix_sparse.hpp.</p>
<h4>Template parameters</h4>
<table border="1" summary="parameters">
<tbody>
<tr>
<th>Parameter</th>
<th>Description</th>
<th>Default</th>
</tr>
<tr>
<td><code>T</code></td>
<td>The type of object stored in the coordinate matrix.</td>
<td></td>
</tr>
<tr>
<td><code>F</code></td>
<td>Functor describing the storage organization. <a href=
"#coordinate_matrix_1">[1]</a></td>
<td><code>row_major</code></td>
</tr>
<tr>
<td><code>IB</code></td>
<td>The index base of the coordinate vector. <a href=
"#coordinate_matrix_2">[2]</a></td>
<td><code>0</code></td>
</tr>
<tr>
<td><code>IA</code></td>
<td>The type of the adapted array for indices. <a href=
"#coordinate_matrix_3">[3]</a></td>
<td><code>unbounded_array&lt;std::size_t&gt;</code></td>
</tr>
<tr>
<td><code>TA</code></td>
<td>The type of the adapted array for values. <a href=
"#coordinate_matrix_3">[3]</a></td>
<td><code>unbounded_array&lt;T&gt;</code></td>
</tr>
</tbody>
</table>
<h4>Model of</h4>
<p><a href="container_concept.html#matrix">Matrix</a> .</p>
<h4>Type requirements</h4>
<p>None, except for those imposed by the requirements of <a href=
"container_concept.html#matrix">Matrix</a> .</p>
<h4>Public base classes</h4>
<p><code>matrix_container&lt;coordinate_matrix&lt;T, F, IB, IA,
TA&gt; &gt;</code></p>
<h4>Members</h4>
<table border="1" summary="members">
<tbody>
<tr>
<th>Member</th>
<th>Description</th>
</tr>
<tr>
<td><code>coordinate_matrix ()</code></td>
<td>Allocates a <code>coordinate_matrix</code> that holds at most
zero rows of zero elements.</td>
</tr>
<tr>
<td><code>coordinate_matrix (size_type size1, size_type2, size_type non_zeros = 0)</code></td>
<td>Allocates a <code>coordinate_matrix</code> that holds at most
<code>size1</code> rows of <code>size2</code> elements.</td>
</tr>
<tr>
<td><code>coordinate_matrix (const coordinate_matrix
&amp;m)</code></td>
<td>The copy constructor.</td>
</tr>
<tr>
<td><code>template&lt;class AE&gt;<br />
coordinate_matrix (size_type non_zeros, const
matrix_expression&lt;AE&gt; &amp;ae)</code></td>
<td>The extended copy constructor.</td>
</tr>
<tr>
<td><code>void resize (size_type size1, size_type size2, bool preserve = true)</code></td>
<td>Reallocates a <code>coordinate_matrix</code> to hold at most
<code>size1</code> rows of <code>size2</code> elements. The
existing elements of the <code>coordinate_matrix</code> are
preseved when specified.</td>
</tr>
<tr>
<td><code>size_type size1 () const</code></td>
<td>Returns the number of rows.</td>
</tr>
<tr>
<td><code>size_type size2 () const</code></td>
<td>Returns the number of columns.</td>
</tr>
<tr>
<td><code>const_reference operator () (size_type i, size_type j)
const</code></td>
<td>Returns the value of the <code>j</code>-th element in the
<code>i</code>-th row.</td>
</tr>
<tr>
<td><code>reference operator () (size_type i, size_type
j)</code></td>
<td>Returns a reference of the <code>j</code>-th element in the
<code>i</code>-th row.</td>
</tr>
<tr>
<td><code>coordinate_matrix &amp;operator = (const
coordinate_matrix &amp;m)</code></td>
<td>The assignment operator.</td>
</tr>
<tr>
<td><code>coordinate_matrix &amp;assign_temporary
(coordinate_matrix &amp;m)</code></td>
<td>Assigns a temporary. May change the coordinate matrix
<code>m</code>.</td>
</tr>
<tr>
<td><code>template&lt;class AE&gt;<br />
coordinate_matrix &amp;operator = (const
matrix_expression&lt;AE&gt; &amp;ae)</code></td>
<td>The extended assignment operator.</td>
</tr>
<tr>
<td><code>template&lt;class AE&gt;<br />
coordinate_matrix &amp;assign (const matrix_expression&lt;AE&gt;
&amp;ae)</code></td>
<td>Assigns a matrix expression to the coordinate matrix. Left and
right hand side of the assignment should be independent.</td>
</tr>
<tr>
<td><code>template&lt;class AE&gt;<br />
coordinate_matrix &amp;operator += (const
matrix_expression&lt;AE&gt; &amp;ae)</code></td>
<td>A computed assignment operator. Adds the matrix expression to
the coordinate matrix.</td>
</tr>
<tr>
<td><code>template&lt;class AE&gt;<br />
coordinate_matrix &amp;plus_assign (const
matrix_expression&lt;AE&gt; &amp;ae)</code></td>
<td>Adds a matrix expression to the coordinate matrix. Left and
right hand side of the assignment should be independent.</td>
</tr>
<tr>
<td><code>template&lt;class AE&gt;<br />
coordinate_matrix &amp;operator -= (const
matrix_expression&lt;AE&gt; &amp;ae)</code></td>
<td>A computed assignment operator. Subtracts the matrix expression
from the coordinate matrix.</td>
</tr>
<tr>
<td><code>template&lt;class AE&gt;<br />
coordinate_matrix &amp;minus_assign (const
matrix_expression&lt;AE&gt; &amp;ae)</code></td>
<td>Subtracts a matrix expression from the coordinate matrix. Left
and right hand side of the assignment should be independent.</td>
</tr>
<tr>
<td><code>template&lt;class AT&gt;<br />
coordinate_matrix &amp;operator *= (const AT &amp;at)</code></td>
<td>A computed assignment operator. Multiplies the coordinate
matrix with a scalar.</td>
</tr>
<tr>
<td><code>template&lt;class AT&gt;<br />
coordinate_matrix &amp;operator /= (const AT &amp;at)</code></td>
<td>A computed assignment operator. Divides the coordinate matrix
through a scalar.</td>
</tr>
<tr>
<td><code>void swap (coordinate_matrix &amp;m)</code></td>
<td>Swaps the contents of the coordinate matrices.</td>
</tr>
<tr>
<td><code>true_reference insert_element (size_type i, size_type j, const_reference
t)</code></td>
<td>Inserts the value <code>t</code> at the <code>j</code>-th
element of the <code>i</code>-th row. Duplicates elements are not allowed.</td>
</tr>
<tr>
<td><code>void append_element (size_type i, size_type j, const_reference t)</code></td>
<td>Appends the value <code>t</code> at the <code>j</code>-th element of the <code>i</code>-th row.
Duplicate elements can be appended to a <code>coordinate_matrix</code>. They are merged into a single
arithmetically summed element by the <code>sort</code> function.</td>
</tr>
<tr>
<td><code>void erase_element (size_type i, size_type j)</code></td>
<td>Erases the value at the <code>j</code>-th element of the
<code>i</code>-th row.</td>
</tr>
<tr>
<td><code>void clear ()</code></td>
<td>Clears the coordinate matrix.</td>
</tr>
<tr>
<td><code>const_iterator1 begin1 () const</code></td>
<td>Returns a <code>const_iterator1</code> pointing to the
beginning of the <code>coordinate_matrix</code>.</td>
</tr>
<tr>
<td><code>const_iterator1 end1 () const</code></td>
<td>Returns a <code>const_iterator1</code> pointing to the end of
the <code>coordinate_matrix</code>.</td>
</tr>
<tr>
<td><code>iterator1 begin1 ()</code></td>
<td>Returns a <code>iterator1</code> pointing to the beginning of
the <code>coordinate_matrix</code>.</td>
</tr>
<tr>
<td><code>iterator1 end1 ()</code></td>
<td>Returns a <code>iterator1</code> pointing to the end of the
<code>coordinate_matrix</code>.</td>
</tr>
<tr>
<td><code>const_iterator2 begin2 () const</code></td>
<td>Returns a <code>const_iterator2</code> pointing to the
beginning of the <code>coordinate_matrix</code>.</td>
</tr>
<tr>
<td><code>const_iterator2 end2 () const</code></td>
<td>Returns a <code>const_iterator2</code> pointing to the end of
the <code>coordinate_matrix</code>.</td>
</tr>
<tr>
<td><code>iterator2 begin2 ()</code></td>
<td>Returns a <code>iterator2</code> pointing to the beginning of
the <code>coordinate_matrix</code>.</td>
</tr>
<tr>
<td><code>iterator2 end2 ()</code></td>
<td>Returns a <code>iterator2</code> pointing to the end of the
<code>coordinate_matrix</code>.</td>
</tr>
<tr>
<td><code>const_reverse_iterator1 rbegin1 () const</code></td>
<td>Returns a <code>const_reverse_iterator1</code> pointing to the
beginning of the reversed <code>coordinate_matrix</code>.</td>
</tr>
<tr>
<td><code>const_reverse_iterator1 rend1 () const</code></td>
<td>Returns a <code>const_reverse_iterator1</code> pointing to the
end of the reversed <code>coordinate_matrix</code>.</td>
</tr>
<tr>
<td><code>reverse_iterator1 rbegin1 ()</code></td>
<td>Returns a <code>reverse_iterator1</code> pointing to the
beginning of the reversed <code>coordinate_matrix</code>.</td>
</tr>
<tr>
<td><code>reverse_iterator1 rend1 ()</code></td>
<td>Returns a <code>reverse_iterator1</code> pointing to the end of
the reversed <code>coordinate_matrix</code>.</td>
</tr>
<tr>
<td><code>const_reverse_iterator2 rbegin2 () const</code></td>
<td>Returns a <code>const_reverse_iterator2</code> pointing to the
beginning of the reversed <code>coordinate_matrix</code>.</td>
</tr>
<tr>
<td><code>const_reverse_iterator2 rend2 () const</code></td>
<td>Returns a <code>const_reverse_iterator2</code> pointing to the
end of the reversed <code>coordinate_matrix</code>.</td>
</tr>
<tr>
<td><code>reverse_iterator2 rbegin2 ()</code></td>
<td>Returns a <code>reverse_iterator2</code> pointing to the
beginning of the reversed <code>coordinate_matrix</code>.</td>
</tr>
<tr>
<td><code>reverse_iterator2 rend2 ()</code></td>
<td>Returns a <code>reverse_iterator2</code> pointing to the end of
the reversed <code>coordinate_matrix</code>.</td>
</tr>
</tbody>
</table>
<h4>Notes</h4>
<p><a name="coordinate_matrix_1">[1]</a>
Supported parameters for the storage organization are
<code>row_major</code> and <code>column_major</code>.</p>
<p><a name="coordinate_matrix_2">[2]</a>
Supported parameters for the index base are <code>0</code> and
<code>1</code> at least.</p>
<p><a name="coordinate_matrix_3">[3]</a>
Supported parameters for the adapted array are
<code>unbounded_array&lt;&gt;</code> ,
<code>bounded_array&lt;&gt;</code> and
<code>std::vector&lt;&gt;</code> .</p>
<hr />
<p>Copyright (&copy;) 2000-2002 Joerg Walter, Mathias Koch<br />
   Use, modification and distribution are subject to the
   Boost Software License, Version 1.0.
   (See accompanying file LICENSE_1_0.txt
   or copy at <a href="http://www.boost.org/LICENSE_1_0.txt">
      http://www.boost.org/LICENSE_1_0.txt
   </a>).
</p>
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